Radius capture number of higher-parameter Sierpiński graphs

Determine the radius capture number rc(S(n, k)) of the Sierpiński graph S(n, k) for k ≥ 4.

Background

Theorem 18 determines the radius capture number for Sierpiński graphs S(n, 3), proving rc(S(n, 3)) = rad(S(n, 3)) − 1. The authors report computational examples for k ≥ 4 showing that this equality does not hold in general, including S(3,4) and S(4,4). They explicitly state that the behavior for k ≥ 4 is unresolved and formulate its determination as an open question.